Practice Flashcard 2.5

Front

What is an oblique asymptote?

Back

An oblique asymptote is a slanting line that a graph approaches as the input values (x) go to positive or negative infinity. It occurs when the degree of the numerator is one higher than the degree of the denominator in a rational function.

Front

How do you find the oblique asymptote of a rational function?

Back

To find the oblique asymptote, perform polynomial long division on the rational function. The quotient (ignoring the remainder) will give you the equation of the oblique asymptote.

Front

What are vertical asymptotes?

Back

Vertical asymptotes are lines x = a where a function approaches infinity or negative infinity. They occur at values of x that make the denominator of a rational function equal to zero.

Front

How do you find vertical asymptotes?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Front

What are horizontal asymptotes?

Back

Horizontal asymptotes are lines y = b that a function approaches as x approaches positive or negative infinity. They indicate the end behavior of the function.

Front

How do you find horizontal asymptotes?

Back

To find horizontal asymptotes, compare the degrees of the numerator and denominator: If the degree of the numerator is less, y = 0; if equal, y = leading coefficient of numerator/leading coefficient of denominator; if greater, there is no horizontal asymptote.

Front

What is the significance of asymptotes in graphing functions?

Back

Asymptotes help in understanding the behavior of functions at extreme values and provide guidance on how to sketch the graph accurately.

Front

Back

x = 5, x = 3

Front

What is the equation of the oblique asymptote for the function with the answer y = 3x - 5?

Back

The oblique asymptote is y = 3x - 5.

Front

What are the asymptotes for the function with the answer x = 2, x = -2, y = 1?

Back

The asymptotes are x = 2, x = -2, and y = 1.